Small Cubed Mailsuite 2019 0 1 Liter

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Cubic metre
One cubic metre of concrete (representing the world annual production per inhabitant).
General information
Unit systemSI
Unit ofvolume
Symbolm³ or ㎥
Look up cubic metre in Wiktionary, the free dictionary.

The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the SI derived unit of volume.[1] Its SI symbol is m3.[1] It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, still sometimes used for dry measure (for instance, in reference to wood). Another alternative name, no longer widely used, was the kilolitre.

Conversions[edit]

Some SI units of volume to scale and approximate corresponding mass of water
1 cubic metre= 1000litres (exactly)[2][3]
≈ 35.3 cubic feet
≈ 1.31 cubic yards
≈ 6.29 oil barrels
≈ 220 imperialgallons
≈ 264 US fluid gallons

A cubic metre of pure water at the temperature of maximum density (3.98 °C) and standard atmospheric pressure (101.325 kPa) has a mass of 1000 kg, or one tonne. At 0 °C, the freezing point of water, a cubic metre of water has slightly less mass, 999.972 kilograms.

It is sometimes abbreviated to cu m, m3, M3, m^3, m**3, CBM, cbm when superscriptcharacters or markup cannot be used (e.g. in some typewritten documents and postings in Usenet newsgroups). The 'cubic metre' symbol is encoded by Unicode at code point U+33A5SQUARE M CUBED ❱.[4]

Multiples and submultiples[edit]

Multiples[edit]

Cubic decametre
the volume of a cube of side length one decametre (10 m)
equal to a megalitre
1 dam3 = 1000 m3 = 1 ML
Cubic hectometre
the volume of a cube of side length one hectometre (100 m)
equal to a gigalitre
in civil engineering abbreviated MCM for million cubic metres
1 hm3 = 1000000 m3 = 1 GL
Cubic kilometre
the volume of a cube of side length one kilometre (1000 m)
equal to a teralitre
1 km3 = 1000000000 m3 = 1 TL (810713.19 acre-feet; 0.239913 cubic miles)

Submultiples[edit]

Cubic decimetre
the volume of a cube of side length one decimetre (0.1 m)
equal to a litre
1 dm3 = 0.001 m3 = 1 L
(also known as DCM (=Deci Cubic Meter) in Rubber compound processing)
Cubic centimetre[5]
the volume of a cube of side length one centimetre (0.01 m)
equal to a millilitre
1 cm3 = 0.000001 m3 = 10−6 m3 = 1 mL
Cubic millimetre
the volume of a cube of side length one millimetre (0.001 m)
equal to a microlitre
1 mm3 = 0.000000001 m3 = 10−9 m3 = 1 µL

Notes[edit]

  1. ^ abBureau International de Poids et Mesures. 'Derived units expressed in terms of base unitsArchived 2012-07-16 at the Wayback Machine'. 2014. Accessed 7 August 2014.
  2. ^From 1901 to 1964 the litre was defined as the volume of one kilogram of pure water at 4°C and 760 millimetres of mercury pressure. During this time, a litre was about 1.000028 dm3. In 1964 the original definition was reverted to.
  3. ^'Archived copy'. Archived from the original on 2009-10-01. Retrieved 2010-03-05.CS1 maint: archived copy as title (link)
  4. ^Unicode Consortium (2019). 'The Unicode Standard 12.0 – CJK Compatibility ❰ Range: 3300—33FF ❱'(PDF). Unicode.org. Retrieved May 24, 2019.
  5. ^The cubic centimetre is the base unit of volume of the CGS system of units. The colloquial abbreviations 'cc'/'㏄' and 'ccm' are not SI but are common in some contexts such as cooking, engine displacement and medicine.
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Cubic_metre&oldid=1008176814'

The Metric System

Learning Objective(s)

Small Cubed Mailsuite 2019 0 1 Liter

·Describe the general relationship between the U.S. customary units and metric units of length, weight/mass, and volume.

·Define the metric prefixes and use them to perform basic conversions among metric units.

In the United States, both the U.S. customary measurement system and the metric system are used, especially in medical, scientific, and technical fields. In most other countries, the metric system is the primary system of measurement. If you travel to other countries, you will see that road signs list distances in kilometers and milk is sold in liters. People in many countries use words like 'kilometer,' 'liter,' and 'milligram' to measure the length, volume, and weight of different objects. These measurement units are part of the metric system.

Unlike the U.S. customary system of measurement, the metric system is based on 10s. For example, a liter is 10 times larger than a deciliter, and a centigram is 10 times larger than a milligram. This idea of '10' is not present in the U.S. customary system—there are 12 inches in a foot, and 3 feet in a yard…and 5,280 feet in a mile!

So, what if you have to find out how many milligrams are in a decigram? Or, what if you want to convert meters to kilometers? Understanding how the metric system works is a good start.

What is Metric?

The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.

In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. Notice that the word 'meter' is part of all of these units.

The metric system also applies the idea that units within the system get larger or smaller by a power of 10. This means that a meter is 100 times larger than a centimeter, and a kilogram is 1,000 times heavier than a gram. You will explore this idea a bit later. For now, notice how this idea of 'getting bigger or smaller by 10' is very different than the relationship between units in the U.S. customary system, where 3 feet equals 1 yard, and 16 ounces equals 1 pound.

The table below shows the basic units of the metric system. Note that the names of all metric units follow from these three basic units.

Length

Mass

Volume

basic units

meter

gram

liter

other units you may see

kilometer

kilogram

dekaliter

centimeter

centigram

centiliter

millimeter

milligram

milliliter

In the metric system, the basic unit of length is the meter. A meter is slightly larger than a yardstick, or just over three feet.

The basic metric unit of mass is the gram. A regular-sized paperclip has a mass of about 1 gram.

Among scientists, one gram is defined as the mass of water that would fill a 1-centimeter cube. You may notice that the word 'mass' is used here instead of 'weight.' In the sciences and technical fields, a distinction is made between weight and mass. Weight is a measure of the pull of gravity on an object. For this reason, an object's weight would be different if it was weighed on Earth or on the moon because of the difference in the gravitational forces. However, the object's mass would remain the same in both places because mass measures the amount of substance in an object. As long as you are planning on only measuring objects on Earth, you can use mass/weight fairly interchangeably—but it is worth noting that there is a difference!

Finally, the basic metric unit of volume is the liter. A liter is slightly larger than a quart.

The handle of a shovel is about 1 meter.

A paperclip weighs about 1 gram.

A medium-sized container of milk is about 1 liter.

Though it is rarely necessary to convert between the customary and metric systems, sometimes it helps to have a mental image of how large or small some units are. The table below shows the relationship between some common units in both systems.

Common Measurements in Customary and Metric Systems

Length

1 centimeter is a little less than half an inch.

1.6 kilometers is about 1 mile.

1 meter is about 3 inches longer than 1 yard.

Mass

1 kilogram is a little more than 2 pounds.

28 grams is about the same as 1 ounce.

Volume

1 liter is a little more than 1 quart.

4 liters is a little more than 1 gallon.

The metric system is a base 10 system. This means that each successive unit is 10 times larger than the previous one.

The names of metric units are formed by adding a prefix to the basic unit of measurement. To tell how large or small a unit is, you look at the prefix. To tell whether the unit is measuring length, mass, or volume, you look at the base.

Prefixes in the Metric System

kilo-

hecto-

deka-

meter

gram

liter

deci-

centi-

milli-

1,000 times larger than base unit

100 times larger than base unit

10 times larger than base unit

base units

10 times smaller than base unit

100 times smaller than base unit

1,000 times smaller than base unit

Using this table as a reference, you can see the following:

·A kilogram is 1,000 times larger than one gram (so 1 kilogram = 1,000 grams).

·A centimeter is 100 times smaller than one meter (so 1 meter = 100 centimeters).

·A dekaliter is 10 times larger than one liter (so 1 dekaliter = 10 liters).

Here is a similar table that just shows the metric units of measurement for mass, along with their size relative to 1 gram (the base unit). The common abbreviations for these metric units have been included as well.

Measuring Mass in the Metric System

kilogram

(kg)

hectogram

(hg)

dekagram

(dag)

gram

(g)

decigram

(dg)

centigram

(cg)

milligram

(mg)

1,000 grams

100 grams

10 grams

gram

0.1 gram

0.01 gram

0.001 gram

Since the prefixes remain constant through the metric system, you could create similar charts for length and volume. The prefixes have the same meanings whether they are attached to the units of length (meter), mass (gram), or volume (liter).

Which of the following sets of three units are all metric measurements of length?

A) inch, foot, yard

B) kilometer, centimeter, millimeter

C) kilogram, gram, centigram

D) kilometer, foot, decimeter

Converting between metric units of measure requires knowledge of the metric prefixes and an understanding of the decimal system—that's about it.

For instance, you can figure out how many centigrams are in one dekagram by using the table above. One dekagram is larger than one centigram, so you expect that one dekagram will equal many centigrams.

In the table, each unit is 10 times larger than the one to its immediate right. This means that 1 dekagram = 10 grams; 10 grams = 100 decigrams; and 100 decigrams = 1,000 centigrams. So, 1 dekagram = 1,000 centigrams.

Example

Problem

How many milligrams are in one decigram?

Identify locations of milligrams and decigrams.

Decigrams (dg) are larger than milligrams (mg), so you expect there to be many mg in one dg.

×10

×10

kg

hg

dag

g

dg

cg

mg

^

^

→ →

Dg is 10 times larger than a cg, and a cg is 10 times larger than a mg.

Since you are going from a larger unit to a smaller unit, multiply.

1 dg · 10 · 10 = 100 mg

Multiply: 1 · 10 · 10, to find the number of milligrams in one decigram.

Answer

There are 100 milligrams (mg) in 1 decigram (dg).

Example

Problem

Convert 1 centimeter to kilometers.

Identify locations of kilometers and centimeters.

Kilometers (km) are larger than centimeters (cm), so you expect there to be less than one km in a cm.

÷10

÷10

÷10

÷10

÷10

km

hm

dam

m

dm

cm

mm

^

^

← ← ← ← ←

Cm is 10 times smaller than a dm; a dm is 10 times smaller than a m, etc.

Since you are going from a smaller unit to a larger unit, divide.

1 cm ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 0.00001 km

Divide: 1 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10, to find the number of kilometers in one centimeter.

Answer

1 centimeter (cm) = 0.00001 kilometers (km).

Once you begin to understand the metric system, you can use a shortcut to convert among different metric units. The size of metric units increases tenfold as you go up the metric scale. The decimal system works the same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. By applying what you know about decimals to the metric system, converting among units is as simple as moving decimal points.

Here is the first problem from above: How many milligrams are in one decigram? You can recreate the order of the metric units as shown below:

Small cubed mailsuite 2019 0 1 liter cubic inches

This question asks you to start with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the right of decigrams. You can just move the decimal point two places to the right to convert decigrams to milligrams: .

The same method works when you are converting from a smaller to a larger unit, as in the problem: Convert 1 centimeter to kilometers.

Note that instead of moving to the right, you are now moving to the left—so the decimal point must do the same: .

How many milliliters are in 1 liter?

A) 0.001

B) 0.1

C) 100

D) 1,000

Summary

Small Cubed Mailsuite 2019 0 1 Liter Cubic Inches

The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram. Units in the metric system are all related by a power of 10, which means that each successive unit is 10 times larger than the previous one. This makes converting one metric measurement to another a straightforward process, and is often as simple as moving a decimal point. It is always important, though, to consider the direction of the conversion. If you are converting a smaller unit to a larger unit, then the decimal point has to move to the left (making your number smaller); if you are converting a larger unit to a smaller unit, then the decimal point has to move to the right (making your number larger).





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